Damage Limits of $\text{Nb-Ti}$ and $\text{Nb}_{3}\text{Sn}$ Superconductors Due to High-Intensity Beam Impact

High-energy hadron colliders with multi-TeV centre-of-mass energies require high-field superconducting magnets. Examples include the large hadron collider (LHC) and its high-luminosity upgrade (HL-LHC), as well as future projects such as the future circular collider (FCC-hh) and super proton–proton collider (SPPC). During operation, these magnets are exposed to primary and secondary particles from beam losses. Steady-state losses cause long-term radiation ageing, while sudden equipment failures can deposit large energy in magnet components. Understanding critical current degradation in superconductors under such conditions is essential for magnet design, development, and defining machine protection limits. Experiments were conducted at CERN’s HiRadMat facility, where 440 GeV/c high-intensity proton beams were directly impacted on $\text{Nb-Ti}$ and $\text{Nb}_{3}\text{Sn}$ superconductors at < 5.5 K. Short strand samples were tested first, followed by racetrack coil assemblies. Superconducting performance was assessed via critical transport current and critical field, complemented by optical and electron microscopy. Degradation was correlated with deposited energy density, peak temperature, temperature gradient, and mechanical strain. For the first time, damage limits in thermo-mechanical terms are presented. $\text{Nb-Ti}$ strands and coils showed no degradation up to 1092 K. A reversible “memory loss” in $\text{Nb-Ti}$ coils above 335 K was linked to strand movement. $\text{Nb}_{3}\text{Sn}$ strands exhibited up to 88% critical current loss for transverse temperature gradients of 196 K/mm or residual plastic strain > 0.42%. In $\text{Nb}_{3}\text{Sn}$ coils, memory loss occurred above 209 K, with no permanent degradation up to 695 K and 0.42% strain.